Barut-Girardello and Gilmore-Perelomov coherent states for pseudoharmonic oscillators and their nonclassical properties: Factorization method

In this paper we try to introduce the ladder operators associated with the pseudoharmonic oscillator, after solving the corresponding Schrrdinger equation by using the factorization method. The obtained generalized raising and lowering operators naturally lead us to the Dirac representation space of the system which is much easier to work with, in comparison to the functional Hilbert space. The SU（1, 1） dynamical symmetry group associated with the considered system is exactly established through investigating the fact that the deduced operators satisfy appropriate commutation relations. This result enables us to construct two important and distinct classes of Barut-Girardello and Gilmore-Perelomov coherent states associated with the system. Finally, their identities as the most important task are exactly resolved and some of their nonclassical properties are illustrated, numerically.

Hong–Ou–Mandel interference with two independent weak coherent states

Recently, the Hong-Ou-Mandel （HOM） interference between two independent weak coherent pulses （WCPs） has been paid much attention due to the measurement-device-independent （MDI） quantum key distribution （QKD）. Using classical wave theory, articles reported before show that the visibility of this kind of HOM-type interference is 〈 50%. In this work, we analyze this kind of interference using quantum optics, which reveals more details compared to the wave theory. Analyses confirm the maximum visibility of 50%. And we conclude that the maximum visibility of 50% comes from the two single-photon states in WCPs, without considering the noise. In the experiment, we successfully approach the visibility of 50% by using WCPs splitting from the single pico-second laser source and phase scanning. Since this kind of HOM interference is immune to slow phase fluctuations, both the realized and proposed experiment designs can provide stable ways of high-resolution optical distance detection.

The Wigner function and phase properties of superposition of two coherent states with the vacuum state

This paper discusses some statistical properties of the superposition of two coherent states with a vacuum state, such as sub-Poissonian photon statistics and negativity of the Wigner function. Phase probability distribution and phase variance are calculated. Special cases of the constructed superposition states are presented. The results show that depending on the vacuum state coefficient γ and the coherent state coefficient a, it can generate a variety of nonclassical states.

Amplitude-squared squeezing of superposition of coherent states

This paper discusses the amplitude-squared squeezing for the superposition of two coherent states with their phase differences being separately π/2, 3π/2, and π1, as well as for the superposition state of two pseudoclassical states. According to the analysis, it is found that the superposition state of two coherent states with their phase differences π/2 and 3π/2, and the superposition state of two pseudoclassical states both do exhibit the amplitude-squared squeezing. Also, some specific states are found to exhibit even stronger squeezing effects when relative phase of the superposition is equal to the average photon number. Amplitude-squared squeezing is dependent on the difference in phase between two coherent states.

Using Coherent States to Make Physically Correct Classical-to-Quantum Procedures That Help Resolve Nonrenomalizable Fields Including Einstein’s Gravity

Canonical quantization covers a broad class of classical systems, but that does not include all the problems of interest. Affine quantization has the benefit of providing a successful quantization of many important problems including the quantization of half-harmonic oscillators [1], non-renormalizable scalar fields, such as (ϕ12)3 [2] and (ϕ12)3 [3], as well as the quantum theory of Einstein’s general relativity [4]. The features that distinguish affine quantization are emphasized, especially, that affine quantization differs from canonical quantization only by the choice of classical variables promoted to quantum operators. Coherent states are used to ensure proper quantizations are physically correct. While quantization of non-renormalizable covariant scalars and gravity are difficult, we focus on appropriate ultralocal scalars and gravity that are fully soluble while, in that case, implying that affine quantization is the proper procedure to ensure the validity of affine quantizations for non-renormalizable covariant scalar fields and Einstein’s gravity.

Quantum statistical properties of photon-added spin coherent states

The photon-added spin coherent state as a new kind of coherent state has been defined by iterated actions of the proper raising operator on the ordinary spin coherent state. In this paper, the quantum statistical properties of photon-added spin coherent states such as photon number distribution, second-order correlation function and Wigner function are studied. It is found that the Wigner function shows the negativity in some regions and the second-order correlation function is less than unity. Therefore, the photon-added spin coherent state is a nonclassical state.

Maximal entanglement from photon-added nonlinear coherent states via unitary beam splitters

In this paper, we construct photon-added f-deformed coherent states （PAf-DCSs） for nonlinear bosonic fields by discussing Klauder＇s minimal set of conditions required to obtain coherent states. Using this set of nonlinear states, we propose a very useful scheme for generating the maximal amount of entanglement via unitary beam splitters for different strength regimes of the input field α, deformation q and excitation number m. Therefore, the possibility to create highly entangled states and to control the entanglement is proposed. Moreover, the condition for a maximal and separable output beam state is obtained. Finally, we examine the statistical properties of the PAf-DCSs through the Mandel parameter and exploit a connection between this quantity and the behavior variation of the output state entanglement. Our result may open new perspectives in different tasks of quantum information processing.

Wave packet dynamics of nonlinear Gazeau–Klauder coherent states of a position-dependent mass system in a Coulomb-like potential

AD = 1 position-dependent mass approach to constructing nonlinear quantum states for a modified Coulomb potential is used to generate Gazeau–Klauder coherent states. It appears that their energy eigenvalues are scaled down by the quantum number and the nonlinearity coefficient. We study the basic properties of these states, which are found to be undefined on the whole complex plane, and some details of their revival structure are discussed.

Quantum dual signature scheme based on coherent states with entanglement swapping

A novel quantum dual signature scheme, which combines two signed messages expected to be sent to two diverse receivers Bob and Charlie, is designed by applying entanglement swapping with coherent states. The signatory Alice signs two different messages with unitary operations（corresponding to the secret keys） and applies entanglement swapping to generate a quantum dual signature. The dual signature is firstly sent to the verifier Bob who extracts and verifies the signature of one message and transmits the rest of the dual signature to the verifier Charlie who verifies the signature of the other message. The transmission of the dual signature is realized with quantum teleportation of coherent states. The analysis shows that the security of secret keys and the security criteria of the signature protocol can be greatly guaranteed.An extensional multi-party quantum dual signature scheme which considers the case with more than three participants is also proposed in this paper and this scheme can remain secure. The proposed schemes are completely suited for the quantum communication network including multiple participants and can be applied to the e-commerce system which requires a secure payment among the customer, business and bank.

Amplitude-squared squeezing of the generalized odd-even coherent states of the anharmonic oscillator in a finite-dimensional Hilbert space

This paper discusses the properties of amplitude-squared squeezing of the generalized odd-even coherent states of anharmonic oscillator in finite-dimensional Hilbert space. It demonstrates that the generalized odd coherent states do exhibit strong amplitude-squared squeezing effects in comparison with the generalized even coherent states.

Realistic teleportation of coherent states using squeezed vacuum states

This paper presents a realistic scheme for the teleportation of coherent states in which a two-mode squeezed vacuum state serves as the quantum channel and the position-sum and momentum-difference of two local modes serve as the measuring observables. The average fidelity of the teleportation of coherent states is derived for finite squeezing parameters and it turns out that fidelity greater than 1/2 cannot be achieved by using a classical channel alone and the probability distribution of the measurement result is a Gaussian distribution around the unknown parameter of the input coherent state with a width given by the squeezing parameter.

The dependence of fidelity on the squeezing parameter in teleportation of the squeezed coherent states

This paper investigates an analytical expression of teleportation fidelity in the teleportation scheme of a single mode of electromagnetic field. The fidelity between the original squeezed coherent state and the teleported one is expressed in terms of the squeezing parameter r and the quantum channel parameter （two-mode squeezed state） p. The results of analysis show that the fidelity increases with the increase of the quantum channel parameter p, while the fidelity decreases with the increase of the squeezing parameter r of the squeezed state. Thus the coherent state （r= O） is the best quantum signal for continuous variable quantum teleportation once the quantum channel is built.

Properties of field quantum entropy evolution in the Jaynes-Cummings model with initial squeezed coherent states field

The properties of the field quantum entropy evolution in a system of a single-mode squeezed coherent state field interacting with a two-level atom is studied by utilizing the complete quantum theory, and we focus our attention on the discussion of the influences of field squeezing parameter γ, atomic distribution angle θ and coupling strength g between the field and the atom on the properties of the evolution of field quantum entropy. The results obtained from numerical calculation indicate that the amplitude of oscillation of field quantum entropy evolution decreases with the increasing of squeezing parameter γ, and that both atomic distribution angle θ and coupling strength g between the field and the atom can influence the periodicity of field quantum entropy evolution.

Two-mode excited entangled coherent states and their entanglement properties

This paper introduces two types of two-mode excited entangled coherent states （TMEECSs） ψ±（（α,m,n））, studies their entanglement characteristics, and investigates the influence of photon excitations on quantum entanglement. It shows that for the state （ψ＋ （α, m, m）} the two-mode photon excitations affect seriously entanglement character while the state [ ψ-（α, m, m）） is always a maximally entangled state, and shows how such states can be produced by using cavity quantum electrodynamics and quantum measurements. It finds that the entanglement amount of the TMEECSs is larger than that of the single-mode excited entangled coherent states with the same photon excitation number.

Generation of superpositions of coherent states for an atomic sample in cavity QED

This paper proposes a scheme for generation of superpositions of coherent states of the effective bosonic mode in a collection of atoms. In the scheme an atomic sample interacts with a slightly detuned cavity mode and a resonant strong classical field. Under ceitain conditions the atomic system evolves from a coherent state to a superposition of coherent states.

Generation of any superposition of coherent states along a straight line via resonant atom-cavity interaction

This paper proposes a scheme for generating arbitrary superpositions of several coherent states along a straight line for a cavity mode. In the scheme, several atoms are sent through a cavity initially in a strong coherent state. The superposition of several coherent states with desired coefficients may be generated if each atom is detected in the excited state after it exits the cavity. The scheme is based on resonant atom-cavity interaction and no classical field is required during and after the atom cavity interaction. Thus, the scheme is very simple and the interaction time is very short, which is important in view of decoherence.

Oscillation behaviour in the photon-number distribution of squeezed coherent states

From the normally ordered form of the density operator of a squeezed coherent state（SCS）,we directly derive the compact expression of the SCS＇s photon-number distribution（PND）.Besides the known oscillation characteristics,we find that the PND is a periodic function with a period of π and extremely sensitive to phase.If the squeezing is strong enough,and the compound phase which is relevant to the complex squeezing and displacement parameters are assigned appropriate values,different oscillation behaviours in PND for even and odd photon numbers appear,respectively.

Effects of photon addition on the quantum nonlocality of squeezed entangled coherent states

Effects of photon addition on the quantum nonlocality of squeezed entangled coherent states for Bell-inequality tests are studied theoretically. By utilizing the method of photon-parity measurement, it is found that photon addition can always increase the degrees of Bell violations within a certain parameter range. A possible scheme for generating photon-added squeezed entangled coherent states is proposed.

Gazeau–Klauder coherent states examined from the viewpoint of diagonal ordering operation technique

In this paper we investigate the Gazeau–Klauder coherent states using a newly introduced diagonal ordering operation technique, in order to examine some of the properties of these coherent states. The results coincide with those obtained from other purely algebraic methods, but the calculations are greatly simplified. We apply the general theory to two cases of Gazeau–Klauder coherent states： pseudoharmonic as well as the Morse oscillators.

The entropic squeezing of superposition of two arbitrary coherent states

In this paper the superpositions of two arbitrary coherent states ｜ψ〉 = α ｜β｜ ＋ be^iψ ｜mβe^iδ〉 are constructed by using the superposition principle of quantum mechanics. The entropic squeezing effects of the quantum states are studied. The numerical results indicate that the amplitudes, the ratio between the amplitudes of two coherent states, the phase difference between the two components and the relative phase of the two coefficients play important roles in the squeezing effects of the position entropy and momentum entropy.